Cornish played for the UCLA Bruins for four years (1986–89) and started all 35 games of his sophomore, junior and senior seasons. He earned first-team All-America honors in 1989 and was a second-team selection in 1988.
Following his collegiate career, Cornish played in the NFL for six seasons. A sixth-round selection by the San Diego Chargers, he played with the Chargers, Dallas Cowboys, Minnesota Vikings, Jacksonville Jaguars and Philadelphia Eagles. He was with Dallas for the 1992 and 1993 seasons, helping the Cowboys win the 1993 and 1994 Super Bowls.
Cornish died of heart disease in his sleep at his home on August 22, 2008. Cornish lived in Southlake, Texas (near Dallas) with his wife Robin, who is a registered nurse in the Dallas area, and their five children (three daughters and two sons).